Analysis in Banach Spaces

This secondvolume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the theory.The first two chapters address the relevant classicalbackground from the theory of Banach spaces, including notionsliketype, cotype, K-convexity and contraction principles. In turn, the next two chapters providea detailed treatment of the theory of R-boundedness and Banach spacevalued square functions developed over the last 20 years. In the last chapter, this content is applied to developthe holomorphic functional calculus of sectorial and bi-sectorial operators in Banachspaces. Given its breadth of coverage, this book will be an invaluable reference to graduatestudents and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.